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Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product

Author

Listed:
  • Zhe Gao

    (School of Mathematics, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

  • Jun-e Feng

    (School of Mathematics, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

Abstract

Nonlinear feedback shift registers (NFSRs) are the main components of stream ciphers and convolutional decoders. Recent years have seen an increase in the requirement for information security, which has sparked NFSR research. However, the NFSR study is very imperfect as a result of the lack of appropriate mathematical tools. Many scholars have discovered in recent years that the introduction of semi-tensor products (STP) of matrices can overcome this issue because STP can convert the NFSR into a quasi-linear form. As a result of STP, new NFSR research has emerged from a different angle. In view of this, in order to generalize the latest achievements of NFSRs based on STP and provide some directions for future development, the research results are summarized and sorted out, broadly including the modeling of NFSRs, the analysis of the structure of NFSRs, and the study of the properties of NFSRs.

Suggested Citation

  • Zhe Gao & Jun-e Feng, 2022. "Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product," Mathematics, MDPI, vol. 10(19), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3538-:d:928219
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    References listed on IDEAS

    as
    1. Gao, Bo & Liu, Xuan & Lan, Zhongzhou & Fu, Rongrong, 2018. "A novel method for reconstructing period with single input in NFSR," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 36-40.
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    Cited by:

    1. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.

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